Nonlinear Fokker–Planck Equations with Time-Dependent Coefficients
Barbu V, Röckner M (2023)
SIAM Journal on Mathematical Analysis 55(1): 1-18.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Barbu, Viorelc;
Röckner, MichaelUniBi
Einrichtung
Abstract / Bemerkung
An operator-based approach is used here to prove the existence and uniqueness of u(t, x)) + div(b(t, x, u(t, x))u(t, x)) = 0 in (0, oo) \times Rd, u(0, x) = u0(x), x \in Rd in the Sobolev space proved also that if u0 is a density of a probability measure, so is u(t, & BULL;) for all t \geq 0. Moreover, we construct a weak solution to the McKean-Vlasov SDE associated with the Fokker-Planck equation such that u(t) is the density of its time marginal law.
Stichworte
Fokker-Planck equation;
Cauchy problem;
stochastic differential;
equation;
Sobolev space
Erscheinungsjahr
2023
Zeitschriftentitel
SIAM Journal on Mathematical Analysis
Band
55
Ausgabe
1
Seite(n)
1-18
ISSN
0036-1410
eISSN
1095-7154
Page URI
https://pub.uni-bielefeld.de/record/2982779
Zitieren
Barbu V, Röckner M. Nonlinear Fokker–Planck Equations with Time-Dependent Coefficients. SIAM Journal on Mathematical Analysis. 2023;55(1):1-18.
Barbu, V., & Röckner, M. (2023). Nonlinear Fokker–Planck Equations with Time-Dependent Coefficients. SIAM Journal on Mathematical Analysis, 55(1), 1-18. https://doi.org/10.1137/21M145481X
Barbu, Viorelc, and Röckner, Michael. 2023. “Nonlinear Fokker–Planck Equations with Time-Dependent Coefficients”. SIAM Journal on Mathematical Analysis 55 (1): 1-18.
Barbu, V., and Röckner, M. (2023). Nonlinear Fokker–Planck Equations with Time-Dependent Coefficients. SIAM Journal on Mathematical Analysis 55, 1-18.
Barbu, V., & Röckner, M., 2023. Nonlinear Fokker–Planck Equations with Time-Dependent Coefficients. SIAM Journal on Mathematical Analysis, 55(1), p 1-18.
V. Barbu and M. Röckner, “Nonlinear Fokker–Planck Equations with Time-Dependent Coefficients”, SIAM Journal on Mathematical Analysis, vol. 55, 2023, pp. 1-18.
Barbu, V., Röckner, M.: Nonlinear Fokker–Planck Equations with Time-Dependent Coefficients. SIAM Journal on Mathematical Analysis. 55, 1-18 (2023).
Barbu, Viorelc, and Röckner, Michael. “Nonlinear Fokker–Planck Equations with Time-Dependent Coefficients”. SIAM Journal on Mathematical Analysis 55.1 (2023): 1-18.
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